Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 1 (non-calculator)
The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
Non-calculatorGCSE Foundation
GCSE Foundation sample Paper 1 (non-calculator)
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- 1.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.
- 2.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
- 3.Write the ratio 18:22 in its simplest form.
- 4.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.
- 5.The probability that Kofi passes his driving test on any attempt is 0.6, and each attempt is independent of the others. Work out the probability that he fails both his first two attempts.
- 6.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.
- 7.Given that 2⁵ = 32, work out 2⁶.
- 8.Which of these is a term, rather than a whole expression, an equation, or a formula?
- 9.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.
- 10.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?
- 11.150 pupils are asked about swimming and cycling, and the results are recorded on a frequency tree. The first pair of branches splits the 150 pupils into 90 who swim and 60 who do not swim. Of the 90 who swim, 54 also cycle. Of the 60 who do not swim, 18 cycle. Work out P(S ∩ C), the probability that a pupil, chosen at random, swims and cycles. Give your answer as a fraction in its simplest form.
- 12.Which of these numbers lies between −4 and −1 on a number line?
- 13.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
- 14.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.
- 15.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.
- 16.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.
- 17.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.
- 18.A plan of a garden is drawn to a scale of 1 : 200. A path measures 3 cm on the plan. Work out the real length of the path, in centimetres.
- 19.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.
- 20.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?
How the 20 questions are shared out
- Number — 5 questions (25% of the qualification)
- Algebra — 4 questions (20% of the qualification)
- Ratio, proportion and rates of change — 5 questions (25% of the qualification)
- Geometry and measures — 3 questions (15% of the qualification)
- Probability — 2 questions (7.5% of the qualification)
- Statistics — 1 question (7.5% of the qualification)
Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.